SymPy | Permutation.rank() in Python

Permutation.rank() : rank() is a sympy Python library function that returns the lexicographic rank of the permutation.

Syntax : sympy.combinatorics.permutations.Permutation.rank()

Return : lexicographic rank of the permutation



Code #1 : rank() Example

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# Python code explaining
# SymPy.Permutation.rank()
  
# importing SymPy libraries
from sympy.combinatorics.partitions import Partition
from sympy.combinatorics.permutations import Permutation
  
# Using from sympy.combinatorics.permutations.Permutation.rank() method 
  
# creating Permutation
a = Permutation([[2, 0], [3, 1]])
  
b = Permutation([1, 3, 5, 4, 2, 0])
  
  
print ("Permutation a - rank form : ", a.rank())
print ("Permutation b - rank form : ", b.rank())

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Output :

Permutation a – rank form : 16
Permutation b – rank form : 191

Code #2 : rank() Example – 2D Permutation

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# Python code explaining
# SymPy.Permutation.rank()
  
# importing SymPy libraries
from sympy.combinatorics.partitions import Partition
from sympy.combinatorics.permutations import Permutation
  
# Using from sympy.combinatorics.permutations.Permutation.rank() method 
  
# creating Permutation
a = Permutation([[2, 4, 0], 
                 [3, 1, 2],
                 [1, 5, 6]])
  
  
print ("Permutation a - rank form : ", a.rank())

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Output :

Permutation a – rank form : 2461




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